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Regularity inheritance in pseudorandom graphs
(Wiley, 2020)
Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox, and Zhao. These inheritance lemmas also imply ...
Regularity inheritance in pseudorandom graphs
(John Wiley and Sons Ltd, 2020)
Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox, and Zhao. These inheritance lemmas also imply ...
The approximate Loebl-Komlós-Sós conjecture II: The rough structure of LKS graphs
(Society for Industrial and Applied Mathematics, 2017)
This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph ...
Regular queries on graph databases
(Springer, 2017)
Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes ...
The approximate Loebl-Komlós-Sós conjecture III: The finer structure of LKS graphs
(Society for Industrial and Applied Mathematics, 2017)
This is the third of a series of four papers in which we prove the following relaxation ofthe Loebl–Komlós–S ́os Conjecture: For everyα >0 there exists a numberk0such that foreveryk > k0everyn-vertex ...
The approximate Loebl-Komlós-Sós conjecture I: The sparse decomposition
(Society for Industrial and Applied Mathematics Publications, 2017)
In a series of four papers we prove the following relaxation of the Loebl–Koml ́os–S ́os Con-jecture: For everyα >0 there exists a numberk0such that for everyk > k0everyn-vertexgraphGwith at least (12+α)nvertices of degree ...
The approximate loebl-komlos-sos conjecture and embedding trees in sparse graphs
(Amer Inst Mathematical Sciences, 2015)
Loebl, Komlos and Sos conjectured that every n-vertex graph G with at least n/2 vertices of degree at least k contains each tree T of order k + 1 as a subgraph. We give a sketch of a proof of the approximate version of ...
The approximate Loebl-Komlós-Sós conjecture IV: Embedding techniques and the proof of the main result
(Society for Industrial and Applied Mathematics Publications, 2017)
This is the last of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph G ...
Regular graph construction for semi-supervised learning
(IOP PublishingBristol, 2014)
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of ...
Edge-colouring of join graphs
(Elsevier Science BvAmsterdamHolanda, 2006)